Provided are: a novel polymerization technique by which a polymer having a controlled molecular weight or molecular weight distribution or a polymer having a desirably regulated, complicated structure can be obtained using commercially available general-purpose materials without using any radical polymerization initiator, or any special material for use in living radical polymerization and without requiring any strict polymerization conditions; a radical polymerization initiation group-containing compound for use in the technique; and a polymer obtained thereby. Specifically, provided are: a method for producing a polymer, the method including a polymerization step of mixing and warming (1) a radically polymerizable monomer, (2) an organic compound having at least one group introduced in a molecule thereof, the group functioning as a polymerization initiation group for the monomer and having a structure represented by formula 1, and (3) a chloride ion-containing and/or bromide ion-containing compound selected from among specific compounds, thereby initiating radical polymerization from the group having the structure, the radical polymerization accompanying a termination reaction; a radical polymerization initiation group-containing compound; and a polymer.